It is known that 1,2,2,2-tetrafluoroethyl difluoromethyl ether, also called desflurane, is an important inhalation anesthetic. This inhalation anesthetic compound is very low in in-vivo metabolism and thus is widely used as a biologically friendly and highly safe drug. One known production method of desflurane is to fluorinate its precursor compound such as 1-chloro-2,2,2-trifluoroethyl difluoromethyl ether (CF3CHClOCHF2; also called isoflurane), 2,2,2-trifluoroethyl difluoromethyl ether (CF3CH2OCHF2) or 1,2,2,2-tetrafluoroethyl dichloromethyl ether (CF3CHFOCHCl2). There is known a method of halogen-exchange fluorination of isoflurane with the use of an alkali metal fluoride (see Patent Document 1), with the use of bromine trifluoride (see Patent Documents 2 and 3) or with the use of hydrogen fluoride (see Patent Documents 3, 4, 5 and 6). There is known a method of direct fluorination of 2,2,2-trifluoroethyl difluoromethyl ether with the use of fluorine gas (see Patent Document 8) or with the use of a high-order metal fluoride compound (see Patent Documents 9 and 10). There is known a method of fluorination of 1,2,2,2-tetrafluoroethyl dichloromethyl ether with the use of hydrogen fluoride (see Patent Document 11).